It is possible, that even a more pacifist type player will be engaged in war mainly because they will be forced to defend themselves.
Still, I understand the OP concern. In sandbox games, theoretically, you can set your opponents and such that "war" would hardly be a feature. Even cultural incursion wold not be necessary if you just forge alliances with everyone. (I'd be surprised if many people play this way... it sort of removes much of the fun of features like ship design which really wouldn't matter in a game like that).
Overall, however, the naming of the just seems to leave the door open to too many situations where what is happening doesn't match the age - unless there are meta events which trigger changes in gameplay. (But my sense is this not the kind of thing they would do outside of the campaign). I mean, if races spawn close together, widespread war among races can begin far before the 2nd age comes. Or, in a really well balanced game, heated war and buildup might not reach its fiercest until the third age. The idea of Ascension is applicable only if research victories are in play.
In other words, the more I think about it, the more I feel that the naming of the ages has the potential to be incongruous with what is happening in the game (unless the naming of the ages could be flexible and reflect what is happening.)